Question:

An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8:27. The ratio of the radii of the nuclei (assumed to be spherical) is:

2:3

4:9

8:27

3:2

V1/V2 = 8/27
m1V1 = m2V2
m1/m2 = V2/V1 = 27/8
ρ × (4/3)πR1³
ρ × (4/3)πR2³
(R1/R2)³ = (27/8)
(R1/R2) = (27/8)^(1/3) = (3²/2³)^(1/3) = 3/2
R1/R2 = 3/2